What is the width?

Question

The area os a rectangular lobby floor in the new office building is 15x^2+47x+28. The length is 5x+4.

Answer 1

Hi Zarayla, you are given one of the binomials, (5x + 4). All you need to do is find the other one. There are a number of ways to find the other binomial.

 

You can divide 5x + 4 into 15x² + 47x + 28 to get the second binomial.

 

You can use the information given, the one binomial to find the second one. Let's do it that way.

 

Solution:

 

(5x + 4) * (__x + __) = 15x² + 47x + 28

 

What two numbers when multiplied together is equal to 15 given one of the numbers is 5? Answer: 3.

 

(5x + 4) * (3x + __) = 15x² + 47x + 28

 

What two numbers when multiplied together is equal to 28 given one of the numbers is 4? Answer: 7.

 

(5x + 4) * (3x + 7) = 15x² + 47x + 28

 

The solution is: (5x + 4) * (3x + 7).

 

Check:

 

We can use the distributive rule to check our answer.

 

(5x * 3x + 5x * 7) + (4 * 3x + 4 * 7)

 

15x² + 35x + 12x + 28

 

15x² + 47x + 28, the answer checks.

 

Questions?

 

Answer 2

Use AC method,  15x^2+47x+28 can be factored as (5x+4)(3x+7).  Since lenght* width is area and since length is 5x+4, width is 3x+7.